One way is this
ReplaceList[{1, 1, 1, 0, -1, -1, 1, 1, 1, 0, 0, 0, 0, -1, -1},
{___, a : PatternSequence[1, 0 .., -1], ___} :> {a}]
(* {{1, 0, -1}, {1, 0, 0, 0, 0, -1}} *)
If you need the position, length or some other information about the location of the match inside the list, you could do it like this:
ReplaceList[{1, 1, 1, 0, -1, -1, 1, 1, 1, 0, 0, 0, 0, -1, -1},
{s___, a : PatternSequence[1, 0 .., -1], ___} :>
With[{l = Length[{s}]}, {{l + 1, l + Length[{a}]}, {a}}]]
(* {{{3, 5}, {1, 0, -1}}, {{9, 14}, {1, 0, 0, 0, 0, -1}}} *)
This stores the start elements before the matching pattern in s
and you can calculate all information from this. Here, I give the start- and end-position of the pattern inside the list.